In the exploration of earth formations, it is known to move an array of sensors along an exposed surface of the earth formation, typically along the exposed wall of a bore-hole in the earth, to produce data signals representative of variations in certain meaningful characteristics of the adjacent earth formation. For example, this is commonly done in the so-called logging of bore holes, in search of natural deposits of oil. Typically also, the data signals produced by the sensors are in electrical form, or are converted thereto.
A common form of sensor system used for this purpose injects current from an electrode array into the adjacent earth formation and measures variations in that current and/or in a voltage related to the current. It is also possible to use an array of electrodes to sense variations in a potential known as the spontaneous potential or SP, which appears naturally along the explored wall. In either case, the electrical signals vary in accordance with certain characteristics of the adjacent earth formation, and can therefore be used to characterize that formation.
While it is possible to obtain some useful information in such systems which use only a single sensor, significant advantages result from using systems containing an array of multiple sensors to obtain the data signals, and using the data signals so derived to produce a two-dimensional image corresponding to an area of the bore-hole wall extending both along, and at right angles to, the direction of motion of the sensor array. One such system, commonly known as a Formation Microscanner or FMS.TM., conveys to an experienced observer a clearer mental picture of the distribution of the measured characteristic over a segment of the bore-hole wall than does a single-line graph of data produced by a single sensor.
One way in which to collect data to produce a two-dimensional image of a bore-hole wall would be to use a linear array of sensors, i.e., one in which the sensors are all distributed along a straight line, at right angle to the direction of motion of the array. In this way, the data collected would span two dimensions: at any given time the array of sensors would be collecting data along the azimuth direction (i.e., the direction transverse to the array motion along the bore-hole wall) and, over time, the array would be moved to successive different positions along the bore-hole wall.
In any sensor system, the individual sensors need to be sufficiently separated one from another to reduce the possibility that the sensors will interfere with one another in their operation; for example, sensor electrodes will electrically short-circuit to each other if they are placed too close together in the array. However, a deleterious result of such sensor separation in a linear array is the decrease in the resolution of the final image in the azimuth direction, or an increase in undesirable aliasing problems; in this connection see U.S. Pat. No. 4,567,759 of Ekstrom et al, issued Feb. 4, 1986.
One way to accommodate the sensor separation requirement and still achieve satisfactory azimuth resolution is to use a system in which the array of sensors is distributed in a two-dimensional pattern, so that the sensors span the azimuth direction with increased resolution (i.e., there are a larger number of sensors per unit of distance along the azimuth direction) while still being sufficiently separated one from another. One such sensor pattern positions the sensors across the array in a zig-zag pattern, whereby the sensors are very closely spaced, or even overlapping, along the azimuth direction, but are separated into rows such that adjacent azimuth sensors are in different rows. As such a sensor array is pulled along the bore-hole wall, the sensor array sweeps out a continuous, or more nearly continuous, area of the bore-hole wall than if a single row of sensors was used, and yet provides the necessary separation between electrodes.
At any given time, the array of sensors will be producing data corresponding to different positions on the bore-hole wall, both in the azimuth direction and in the logging direction, corresponding to the different positions of the sensors distributed on the face of the probe. For simplicity, position along the logging direction will be referred to herein as "depth," even though the logging direction is not necessarily limited to being purely vertical. In order to achieve maximal resolution, these different positions need to be taken into account when the data is presented in image form. More particularly, the depths associated with the sensor data from individual sensors need to be adjusted to ensure that all the data are presented for depths corresponding to those at which the sensors were when the data was produced. A system of this type using depth adjustment of the data is described, for example, in the above cited Ekstrom et al patent.
While two-dimensional display systems have proved to be effective for their intended purposes, as with nearly all measuring systems their maximum useful sensitivity and accuracy is limited by the presence in the data signals of variations which do not represent the characterics to be detected. Such undesired, false, or spurious signal components will be designated herein as "noise," to distinguish them from "true" data signals, without thereby suggesting that they are necessarily random.
When the desired, true data signals are large compared to the level of noise, noise is not as much of a problem as when the desired, true data signals are relatively small. For example, in usual bore-hole exploration, a water-based "mud" is used in the bore-hole which helps to support the bore-hole walls physically, and also provides a medium of rather high electrical conductivity for current flowing between sensors and bore-hole wall. With such a high-conductivity mud, it is relatively easy to obtain data signals sufficiently large compared to the level of noise to be practical for commercial FMS.TM. bore-hole exploration. However, it is sometimes desirable for certain purposes to use an oil-based mud, which has a much lower conductivity than usual water-based muds, and this lower conductivity reduces the strength of the desired, true data signals so that they are more easily obscured by noise signals. Accordingly, in this situation, it is especially desirable to discriminate against noise signals and to reduce their effects on the two-dimensional signal display.
One type of noise which can adversely affect the results of bore-hole exploration is designated herein as "one-dimensional" noise, since it varies primarily as a function of the position of the entire sensor array along its direction of motion, but is substantially the same for all sensor positions in the array. When such one-dimensional noise occurs in a system in which the sensors are distributed in a two-dimensional array, all of the sensors will be affected by the noise at the same time. After the data is depth-adjusted to take into account the vertical distribution of the sensors on the probe face, the noisy data will appear as anomalous artifacts in the final image in the shape of "footprints" of the pattern of sensors in the array. For example, where the sensors extend across the array in a zig-zag pattern, the artifacts are in the form of a corresponding set of zig-zags.
Accordingly, it is an object of the present invention to provide a new and useful signal filtering method and apparatus for reducing or eliminating certain artifacts which may appear in an electrically-derived two-dimensional image of an earth formation due to one-dimensional noise signals present in a two-dimensional array of logging sensors.
Another object is to provide a method and apparatus for reducing or eliminating artifacts of zig-zag form which tend to be produced in such a two-dimensional image by one-dimensional noise signals from a two-dimensional array of logging sensors arranged along zig-zag lines. A further object is to provide a method and apparatus for producing more accurate, and more readily interpreted, two-dimensional images of certain characteristics of a bore-hole wall.